Although K-Nearest Neigbours (KNN) is often regarded as very simple machine learning algorithm, its utility and power are undeniable. It is one of the core algorithms for supervised learning. Simply put, supervised learning is proccess of creating model that can predict a target variable based on input data, using knowledge from dataset where we know the actual values of the target variable. KNN can be effectively used for both classification (target variable can take a limited number of values) and regression (target variable can take on continuous range of values) tasks. The simplest explanation of KNN for classification tasks is that an object is classifed by plurality vote of its k nearest neighbours. For regression tasks, KNN can be generalized so that an object is assigned value that is the average of the values of its k nearest neigbours. However, this is just a basic overview and there are several factors to consider when using KNN to develop an effective machine learning model.
We have chosen Air Quality and Pollution Assesment dataset to show how K-Nearest Neighbours algorithm works. This Dataset is derived from World Health Organization and World Bank Group This Dataset contains several features, in other words, columns, lets go through each one of them and explain what they mean.
Then there is so called Target Variable, thats the variable that we are trying to predict, in our dataset, it is called Air Quality and it can have 4 possible values depending on Air Quality, these values are the following:
As part of data preprocessing we read data from csv file and then we preprocess them. Considering that there are no missing values, there is no need to fill them. All features are already numerical, so there is no need to convert them any further. Target variable can be 4 values, and there is order between those values (it is ordinal categorical datatype), so we convert it into categorical type with order between them. We split data into 3 parts, train, validate and test with train size being 60% of the original dataset and validate and test both being 20% of the original dataset
def preprocess_data(df:pd.DataFrame)->pd.DataFrame:
""" Function, for preprocessing data
"""
qual_category = pd.api.types.CategoricalDtype(categories=['Hazardous', 'Poor', 'Moderate', 'Good'], ordered=True)
df['Air Quality'] = df['Air Quality'].astype(qual_category)
return df
def read_data(path:str='data/data.csv', y:str='Air Quality',**kwargs)->tuple:
""" Function thats read data, and splits them into Train, Validation and Test datasets
also separates, target value from others values.
---
Attributes:
path: [str], path to csv data file
y: [str], name of Target value
kwargs: options, use seed for random_seed
---
Returns:
tuple with Train,Validation,Test parametrs set, Target values: Train, Test, Validation
"""
df = pd.read_csv(path)
display(df.info())
display(df.describe())
df = preprocess_data(df)
# Split the training dataset into train and rest (default 60% : 40%)
Xtrain, Xrest, ytrain, yrest = train_test_split(
df.drop(columns=[y]), df[y], test_size=0.4, random_state=kwargs.get('seed',42))
# Split the rest of the data into validation dataset and test dataset (default: 24% : 16%)
Xtest, Xval, ytest, yval = train_test_split(
Xrest, yrest, test_size=0.5, random_state=kwargs.get('seed',42))
print(f'Dataset: {path} | Target value: {y} | Seed: {kwargs.get('seed',42)}')
return Xtrain, Xtest, Xval, ytrain, ytest, yvalXtrain, Xtest, Xval, ytrain, ytest, yval = read_data(seed=42)<class 'pandas.core.frame.DataFrame'>
RangeIndex: 5000 entries, 0 to 4999
Data columns (total 10 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Temperature 5000 non-null float64
1 Humidity 5000 non-null float64
2 PM2.5 5000 non-null float64
3 PM10 5000 non-null float64
4 NO2 5000 non-null float64
5 SO2 5000 non-null float64
6 CO 5000 non-null float64
7 Proximity_to_Industrial_Areas 5000 non-null float64
8 Population_Density 5000 non-null int64
9 Air Quality 5000 non-null object
dtypes: float64(8), int64(1), object(1)
memory usage: 390.8+ KBNone| Temperature | Humidity | PM2.5 | PM10 | NO2 | SO2 | CO | Proximity_to_Industrial_Areas | Population_Density | |
|---|---|---|---|---|---|---|---|---|---|
| count | 5000.000000 | 5000.000000 | 5000.000000 | 5000.000000 | 5000.000000 | 5000.000000 | 5000.000000 | 5000.000000 | 5000.000000 |
| mean | 30.029020 | 70.056120 | 20.142140 | 30.218360 | 26.412100 | 10.014820 | 1.500354 | 8.425400 | 497.423800 |
| std | 6.720661 | 15.863577 | 24.554546 | 27.349199 | 8.895356 | 6.750303 | 0.546027 | 3.610944 | 152.754084 |
| min | 13.400000 | 36.000000 | 0.000000 | -0.200000 | 7.400000 | -6.200000 | 0.650000 | 2.500000 | 188.000000 |
| 25% | 25.100000 | 58.300000 | 4.600000 | 12.300000 | 20.100000 | 5.100000 | 1.030000 | 5.400000 | 381.000000 |
| 50% | 29.000000 | 69.800000 | 12.000000 | 21.700000 | 25.300000 | 8.000000 | 1.410000 | 7.900000 | 494.000000 |
| 75% | 34.000000 | 80.300000 | 26.100000 | 38.100000 | 31.900000 | 13.725000 | 1.840000 | 11.100000 | 600.000000 |
| max | 58.600000 | 128.100000 | 295.000000 | 315.800000 | 64.900000 | 44.900000 | 3.720000 | 25.800000 | 957.000000 |
Dataset: data/data.csv | Target value: Air Quality | Seed: 42df_original = Xtrain
df_tmp = ytrain.copy()
df_tmp = df_tmp.astype("category")
df_tmp_counts = df_tmp.value_counts()
custom_colors = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728']
fig = plt.figure(figsize=(15,8))
ax1 = fig.add_subplot(1,2,1)
sns.barplot(x = df_tmp_counts.index, y = df_tmp_counts.values, ax = ax1, order=df_tmp_counts.index)
for i, bar in enumerate(ax1.patches):
bar.set_facecolor(custom_colors[i])
ax1.set_xlabel("Air quality type", fontsize = 13)
ax1.set_ylabel("Frequency",fontsize = 13)
ax1.set_title("Air quality Frequency in Train dataset",fontsize = 17)
ax1.grid(axis='y', color='black', alpha=.2, linewidth=.5)
animal_count = df_tmp.value_counts()
ax2 = fig.add_subplot(1,2,2)
ax2.pie(animal_count, labels=animal_count.index,autopct='%.0f%%', textprops={"fontsize": 13})
ax2.set_title("Air quality distribution in Train dataset", fontsize = 17)Text(0.5, 1.0, 'Air quality distribution in Train dataset')
df_original.info()<class 'pandas.core.frame.DataFrame'>
Index: 3000 entries, 4576 to 860
Data columns (total 9 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Temperature 3000 non-null float64
1 Humidity 3000 non-null float64
2 PM2.5 3000 non-null float64
3 PM10 3000 non-null float64
4 NO2 3000 non-null float64
5 SO2 3000 non-null float64
6 CO 3000 non-null float64
7 Proximity_to_Industrial_Areas 3000 non-null float64
8 Population_Density 3000 non-null int64
dtypes: float64(8), int64(1)
memory usage: 234.4 KBfig, axes = plt.subplots(2, 2, figsize=(15, 15))
ax = axes[0,0]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["Temperature"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([int(x) for x in bins])
# Set titles and labels
ax.set_title("Temperature histogram (Train)", fontsize = 17)
ax.set_xlabel("Temperature (°C)", fontsize = 13)
ax.set_ylabel("Frequency", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+2.5, count + 10, int(count), ha="center", va="bottom")
ax = axes[0,1]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["Humidity"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([int(x) for x in bins])
# Set titles and labels
ax.set_title("Humidity histogram (Train)", fontsize = 17)
ax.set_xlabel("Humidity (%)", fontsize = 13)
ax.set_ylabel("Frequency", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+4.5, count + 10, int(count), ha="center", va="bottom")
ax = axes[1,0]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["PM2.5"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([int(x) for x in bins])
# Set titles and labels
ax.set_title("PM2.5 histogram (Train)", fontsize = 17)
ax.set_xlabel("PM2.5 (µg/m³)", fontsize = 13)
ax.set_ylabel("Frequency", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+15.5, count + 10, int(count), ha="center", va="bottom")
ax = axes[1,1]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["PM10"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([int(x) for x in bins])
# Set titles and labels
ax.set_title("PM10 histogram (Train)", fontsize = 17)
ax.set_xlabel("PM10", fontsize = 13)
ax.set_ylabel("Frequency (µg/m³)", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+15.5, count + 10, int(count), ha="center", va="bottom")
fig, axes = plt.subplots(2, 2, figsize=(15, 15))
ax = axes[0,0]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["NO2"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([int(x) for x in bins])
# Set titles and labels
ax.set_title("NO2 histogram (Train)", fontsize = 17)
ax.set_xlabel("NO2 (ppb)", fontsize = 13)
ax.set_ylabel("Frequency", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+2.5, count + 10, int(count), ha="center", va="bottom")
ax = axes[0,1]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["SO2"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([int(x) for x in bins])
# Set titles and labels
ax.set_title("SO2 histogram (Train)", fontsize = 17)
ax.set_xlabel("SO2 (ppb)", fontsize = 13)
ax.set_ylabel("Frequency", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+2.5, count + 10, int(count), ha="center", va="bottom")
ax = axes[1,0]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["CO"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([f'{x:.1f}' for x in bins])
# Set titles and labels
ax.set_title("CO histogram (Train)", fontsize = 17)
ax.set_xlabel("CO (ppm)", fontsize = 13)
ax.set_ylabel("Frequency", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+4.5, count + 10, int(count), ha="center", va="bottom")
ax = axes[1,1]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["Proximity_to_Industrial_Areas"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([int(x) for x in bins])
# Set titles and labels
ax.set_title("Proximity to Industrial Areas histogram (Train)", fontsize = 17)
ax.set_xlabel("Proximity to Industrial Areas (km)", fontsize = 13)
ax.set_ylabel("Frequency", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+1.5, count + 10, int(count), ha="center", va="bottom")
fig, axes = plt.subplots(2, 2, figsize=(13, 13))
ax = axes[0,0]
# Plot the histogram
counts, bins, patches = ax.hist(df_original["Population_Density"], edgecolor="black", color="skyblue")
ax.set_xticks(bins) # Use bins directly for edge ticks
ax.set_xticklabels([int(x) for x in bins])
# Set titles and labels
ax.set_title("Population Density histogram (Train)", fontsize = 17)
ax.set_xlabel("Population Density (people/km²)", fontsize = 13)
ax.set_ylabel("Frequency", fontsize = 13)
for i, count in enumerate(counts):
ax.text(bins[i]+28.5, count + 5, int(count), ha="center", va="bottom")
axes[0,1].set_visible(False)
axes[1,1].set_visible(False)
axes[1,0].set_visible(False)
We are trying to solve supervised learning problem, where based on p features $ X_{1}, …, X_{p}$ (Temperature, Humidity, …) we want to predict the value of target variable \(Y\) (Air Quality). We can put all of these features into vector \(\textbf{X} = (X_{1}, ... X{_p})^T\) which we will interpret as a random vector, and one of its specific realization will be denoted as \(\mathbf{x}\). Let \(\mathcal{X}\) where \(\textbf{x} \in \mathcal{X}\) be set containing all possible values of these features, typically, and in our case, \(\mathcal{X} = \mathbb{R}^p\). Then we can can describe our training dataset as N pairs \((\textbf{x}_{1}, Y_{1}), ..., (\textbf{x}_{p}, Y_{p})\) where \(\textbf{x}_{i}\), respectively \(Y_{i}\) is vector of features, respectively target variable. The basic concept of predicting value of data point \(\mathbf{x} \in \mathcal{X}\) is finding the k-closest points from it (these points come from the train dataset). If we are solving regression problem, we then then the average from the target varibles of the k-closest neighbours, in classification problem (that’s our case) we take the most frequent value from the target variables of the k-closest neighbours.
When trying to find the best model, there are many things to consider. First of all we should define distance function.
Distance also called metric defined on set \(\mathcal{X}\) is function d: \(\mathcal{X} \times \mathcal{X} \rightarrow [0, +\infty)\) such that for all \(x, y, z \in \mathcal{X}\), the following conditions holds:
$ i);d(x,y) $, and \(d(x,y) = 0\) if and only if \(x = y\) (positive definiteness)
$ ii);d(x,y) = d(y,x)$ (symetry)
$ iii);d(x,y) d(x,z) + d(z,y)$ (triangle inequality)
The most common distance function used is KNN is Minkowski distance also called q-norm defined as follows:
\(||x-y||_{q} = d_{q}(x,y) = \sqrt[q]{\sum_{i=1}^{p} (x_i - y_i)^q}\)
After we have found k-nearest neighbours, we need to somehow decide what value we should predict. In our case, we could just precict the value with the most frequent target variable. What we can also do is try weighted voting, that means that closer neighbours will have vote with higher value.
Common choice for weight is inverse distance weighting
\(w_{i} = \frac{1}{d(x,y)}\)
For each category \(c\) of the target variable we count the total weighted vote \(W_{c} = \sum_{Y_i \in \mathcal{N}} w_i \cdot 1(Y_i = c)\)
where \(\mathcal{N}\) is set of target variables of k-nearest neighbours, we then choose $ = W_c $ where \(c\) is every possible category of target variable as our prediction
def train_model(*args,**kwargs):
"""Function, that trains model with specific paraketrs, defined in kwargs.
---
Attributes:
*args: Xtrain,Ytrain
**kwargs: options for training model
---
Return: trained model
"""
X = args[0]
y = args[1]
return KNeighborsClassifier(**kwargs).fit(X,y)color_map = {
'Good': 'green',
'Moderate': 'yellow',
'Poor': 'orange',
'Hazardous': 'red'
}
category_order = ["Good", "Moderate", "Poor", "Hazardous"]def show_graph(X, y_pred, x_ax='Temperature', y_ax='Humidity'):
df_viz = X.copy()
df_viz['Air Quality'] = y_pred
fig = px.scatter(df_viz, x=x_ax, y=y_ax, color='Air Quality', color_discrete_map=color_map,
hover_data=df_viz, title='KNN Visualization',
category_orders={'Air Quality':category_order})
fig.update_layout(
title_font=dict(size=17),
xaxis_title_font=dict(size=13),
yaxis_title_font=dict(size=13)
)
fig.show()n_neighbors_slider = widgets.IntSlider(value=5, min=1, max=20, step=1, description="n_neighbors")
p_slider = widgets.IntSlider(value=5, min=1, max=20, step=1, description="p_metric")
scale = widgets.RadioButtons(
options=['None', 'Standard', 'MinMax'],
description='Choose normalization:',
disabled=False
)
weights = widgets.RadioButtons(
options=['uniform', 'distance'],
description='Chose weight:'
)Interactive KNN visualization
When finding the best model, there are many things to consider. Our goal is to somehow maximize the classification accuracy on new data, that the model has never seen before. Accuracy is defined as
\(\frac{ \text{number of correctly classified}}{ \text{number of all classified}}\) The accuracy which we are trying to maximize is the accurate of how our model built using train dataset will predict on validating dataset. In order to maximize this accuracy, we can try changing the number of neighbours (k), then we can try changing the distance metric, lastly, we can try whether using weighted distance makes any difference. We build our model on combination of these different possibilites and for every one of them we predict the accuracy on validating dataset. We then chose the model with the highest accuracy.
def find_best(*args):
""" Function finding best parametrs for specified data
---
Attributes:
Xtrain, ytrain, Xval, Yval
"""
param_grid = {
'n_neighbors': range(1,15),
'p': range(1,4),
'weights': ['uniform', 'distance']
}
param_comb = ParameterGrid(param_grid)
val_acc = []
train_acc = []
for params in param_comb:
clfKNN = KNeighborsClassifier(**params)
clfKNN.fit(args[0], args[1])
train_acc.append(clfKNN.score(args[0],args[1]))
val_acc.append(clfKNN.score(args[2],args[3]))
return param_comb[np.argmax(val_acc)], train_acc, val_accbest_params_no_scale, train_acc, val_acc = find_best(Xtrain,ytrain,Xval,yval)
scaler = StandardScaler()
Xtrain_fit = scaler.fit_transform(Xtrain)
Xval_fit = scaler.transform(Xval)
best_params_standard, train_acc_standard, val_acc_standard = find_best(Xtrain_fit,ytrain,Xval_fit,yval)
scaler = MinMaxScaler()
Xtrain_fit = scaler.fit_transform(Xtrain)
Xval_fit = scaler.transform(Xval)
best_params_minmax, train_acc_minmax, val_acc_minmax = find_best(Xtrain_fit,ytrain,Xval_fit,yval)Using Min-Max normalization, the best accuracy we get is 08331
clfKNN = KNeighborsClassifier(**best_params_no_scale)
clfKNN.fit(Xtrain, ytrain)
y_knn_val = clfKNN.predict(Xval)
display(metrics.accuracy_score(yval, y_knn_val))0.833fig, ax = plt.subplots(figsize=(15,5))
ax.set_title("Model accuracy on Training and Validating datasets based on hyperparameter index (no normalization)", fontsize=17)
ax.plot(train_acc,'or-')
ax.plot(val_acc,'ob-')
max_idx = np.argmax(val_acc)
ax.plot(max_idx, val_acc[max_idx], marker='o', color='#77DD77', markersize=13, markeredgecolor='black', markeredgewidth=2)
ax.set_xlabel('Hyperparameter index', fontsize=13)
ax.set_ylabel('Accuracy', fontsize=13)
ax.legend(['Train', 'Validate', 'Best validate accuracy'])
One technique that can also help with making the model more accurate is normalization. In some cases, the features are difficult to compare and it is essentially impossible to find a universal measure. This can be addressed by using clever methods to normalize the data using linear transformation. The simplest method used to normalize data is called Min-Max normalization which scales every element in selected feature into interval \([0,1]\). It is defined as follows:
For given feature let’s call his minimal value \(\text{min}_x\) and the maximal value \(\text{max}_x\), then we will define the value \(x_i\) of this feature
\(x_i \leftarrow \frac{ x_i - \text{min}_x}{ \text{max}_i - \text{min}_x}\)
Another commonly used normalization method is standardization, defined as follows \(x_i \leftarrow \frac{x_i - \bar{x}}{\sqrt{s_x^2}}\) where \(\bar{x} = \frac{1}{n} \sum_{i} x_i\) is sample mean and \(s_x^2 = \frac{1}{n-1} \sum_{i}^{} {(x_i - \bar{x})^2}\)
Using Min-Max normalization, the best accuracy we get is 092311
scaler = StandardScaler()
Xtrain_fit = scaler.fit_transform(Xtrain)
Xval_fit = scaler.transform(Xval)
clfKNN = KNeighborsClassifier(**best_params_standard)
clfKNN.fit(Xtrain_fit, ytrain)
y_knn_val = clfKNN.predict(Xval_fit)
display(metrics.accuracy_score(yval, y_knn_val))0.931fig, ax = plt.subplots(figsize=(15,5))
ax.set_title("Model accuracy on Training and Validating datasets based on hyperparameter index (standardization)", fontsize=17)
ax.plot(train_acc_standard,'or-')
ax.plot(val_acc_standard,'ob-')
max_idx = np.argmax(val_acc_standard)
#display(val_acc_standard[max_idx])
ax.plot(max_idx, val_acc_standard[max_idx], marker='o', color='#77DD77', markersize=13, markeredgecolor='black', markeredgewidth=2)
ax.set_xlabel('Hyperparameter index', fontsize=13)
ax.set_ylabel('Accuracy', fontsize=13)
ax.legend(['Train', 'Validate', 'Best validate accuracy'])0.931
Using Min-Max normalization, the best accuracy we get is 0.931
scaler = MinMaxScaler()
Xtrain_fit = scaler.fit_transform(Xtrain)
Xval_fit = scaler.transform(Xval)
clfKNN = KNeighborsClassifier(**best_params_minmax)
clfKNN.fit(Xtrain_fit, ytrain)
y_knn_val = clfKNN.predict(Xval_fit)
display(metrics.accuracy_score(yval, y_knn_val))0.942fig, ax = plt.subplots(figsize=(15,5))
ax.set_title("Model accuracy on Training and Validating datasets based on hyperparameter index (min-max normalization)", fontsize=17)
ax.plot(train_acc_minmax,'or-')
ax.plot(val_acc_minmax,'ob-')
max_idx = np.argmax(val_acc_minmax)
#display(val_acc_minmax[max_idx])
ax.plot(max_idx, val_acc_minmax[max_idx], marker='o', color='#77DD77', markersize=13, markeredgecolor='black', markeredgewidth=2)
ax.set_xlabel('Hyperparameter index', fontsize=13)
ax.set_ylabel('Accuracy', fontsize=13)
ax.legend(['Train', 'Validate', 'Best validate accuracy'])0.942
Based on the results, we can see that the best model is the model that uses Min-Max normalization, uses weighted distance, 3-norm and 3 neighbours with accuracy of 0.942. We can also graph confusion matrix, that shows how accurately we predicted each type of category. Finally, we will predict the expected accuracy on the test dataset, which will give us an estimate of how accurately the model will perform on new, unseen data.
best_params_minmax{'weights': 'distance', 'p': 3, 'n_neighbors': 3}max_idx = np.argmax(val_acc)
max_idx_standard = np.argmax(val_acc_standard)
max_idx_minmax = np.argmax(val_acc_minmax)
labels = ['without_normalization', 'standardization', 'Min-Max']
values = [val_acc[max_idx], val_acc_standard[max_idx_standard], val_acc_minmax[max_idx_minmax]]
fig, ax = plt.subplots()
colors = ['#3498db', '#2ecc71', '#e74c3c']
ax.bar(labels, values, color=colors, edgecolor='black', width=0.5)
ax.set_ylim(0, 1.15)
ax.set_yticks([0, 0.2, 0.4, 0.6, 0.8, 1.0])
ax.set_xlabel("Normalization type", fontsize=14)
ax.set_ylabel("Accuracy", fontsize=14)
ax.set_title("Accuracy of models based on normalization", fontsize=16)
ax.grid(axis='y', linestyle='--', alpha=0.7)
for i, value in enumerate(values):
ax.text(i, value + 0.02, f'{value:.2f}', ha='center', fontsize=12)
plt.show()
from sklearn.metrics import confusion_matrix, ConfusionMatrixDisplay
confusionMatrixDT = metrics.confusion_matrix(yval, y_knn_val)
fig, ax = plt.subplots()
custom_order = ['Good', 'Moderate', 'Poor', 'Hazardous']
confusionMatrixDT = confusion_matrix(yval, y_knn_val, labels=custom_order)
disp = ConfusionMatrixDisplay(confusion_matrix=confusionMatrixDT,
display_labels=custom_order)
disp.plot(ax=ax, cmap="viridis_r")
ax.set_title("Confusion Matrix", fontsize = 17)
ax.set_xlabel("Predicted", fontsize = 13)
ax.set_ylabel("True", fontsize = 13)Text(0, 0.5, 'True')
Our model has 0.921 accuracy on test dateset, this is the accuracy that we can expect on new data
scaler = MinMaxScaler()
Xtrain_fit = scaler.fit_transform(Xtrain)
Xtest_fit = scaler.transform(Xtest)
clfKNN = KNeighborsClassifier(**best_params_minmax)
clfKNN.fit(Xtrain_fit, ytrain)
y_knn_val = clfKNN.predict(Xtest_fit)
display(metrics.accuracy_score(ytest, y_knn_val))0.921https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm
https://www.kaggle.com/datasets/mujtabamatin/air-quality-and-pollution-assessment/data